1. Field of the Invention
This invention relates to stellar attitude determination systems.
2. Description of the Related Art
Commonly used stellar attitude determination systems incorporate measurements from attitude sensors to compute an estimate of spacecraft attitude. The estimate of space-craft attitude is implemented in a form of Kalman filter which employs a data processing algorithm to estimate attitude, with inputs from attitude sensor data. For further detail on Kalman filters generally, see Applied Optimal Estimation, The Analytic Sciences Corporation, Edited by Arthur Gelb, 1974, pages 103-119.
The attitude sensors can include gyroscopes, which provide inertial rate data, and star trackers which provide horizontal and vertical star image positions with signals and generated from a Charge Couple Device array (CCD array). A CCD array is an array of detectors which receive photons from a light source, and convert the detected photons into an electrical signal. The spacecraft attitude is computed in an Attitude Propagation Module, which numerically integrates the compensated gyro data. The Kalman filter, implemented in an Attitude Update Module, computes the attitude correction and gyro bias estimate using the measurement residuals and Kalman filter gains. The measurement residuals, computed in a Star Tracker Data Processing Module, are the difference between the measured star horizontal and vertical positions provided by the star trackers and the estimated star horizontal and vertical positions. The estimated star horizontal and vertical positions are computed using the current attitude estimate. The Kalman filter gains determine the attenuation applied to the filter output.
In the context of star tracker data, the Kalman filter is a low pass filter which outputs attitude correction data. With respect to the inertial rate data, the Kalman filter is a high pass filter used to estimate gyro bias, which is a slowly varying component of the gyro measurement error.
There are two primary sources of error in the determination of attitude: random noise, also known as white noise, and spatial noise. Current art combines both forms of error into temporal noise, which is a pure frequency domain noise that is compensated for by using manufacturer noise specifications in the calculation of measurement residuals. Random noise is caused by random signals generated by the analog electronics as well as background electrical noise, and exists in the frequency domain as temporal noise. Spatial noise, or spatially dependent error, is due to the spatial location of a spacecraft relative to a star detected by the CCD array for purposes of attitude determination. This type of error is deterministic in nature; some factors which can cause this form of error include the particular position on the CCD array of an imaged star, and the spacecraft's motion and speed. Spatial noise can be broken down into two primary components: Low Spatial Frequency (LSF) Error and High Spatial Frequency (HSF) Error. Due to the motion of the spacecraft, both errors affect the frequency domain in the form of temporal noise, such that LSF is converted to low frequency temporal noise, while HSF is converted to high frequency temporal noise. Spatial errors can affect temporal error but are not random in nature; they are actual errors in measurements taken from attitude sensors, dependent upon the spatial conditions of the spacecraft such as its spin, velocity and acceleration.
Currently, white noise is combined with spatial noise in the calculation of Kalman filter gains in attitude determination systems. The manufacturer's error specification consists primarily of a combination of random noise measurements and spatial noise, statically determined at the manufacturer's facility. As spatially dependent errors are determined by such factors as real time spacecraft star tracker CCD array measurements and spacecraft motion, the manufacturer noise specifications are not optimal.
Star tracker and gyroscope white noise is compensated for in filter gain calculations by using a pre-selected measurement noise covariance matrix whose values depend upon the sensor total noise specification supplied by the manufacturer. The Kalman filter uses the pre-selected measurement noise covariance matrix to calculate filter gains, which are used to compute attitude sensor error adjustment data in the form of measurement residuals. The attitude update module uses these measurement residuals to compute attitude correction data, which are supplied to an attitude propagation module within the spacecraft control processor. Because a star tracker contains an additional element of changing spatial conditions which give rise to spatially dependent errors which vary with actual spacecraft conditions, the resulting adjustments to the Kalman filter gain do not provide optimal attitude determination performance.
The common method used today to derive the Kalman filter gain matrix K.sub.c by which the filter is adjusted is given by the following equation: ##EQU1## where ##EQU2## is the total error covariance matrix and P.sup.- denotes the determination of the matrix before a star observation at time t. ##EQU3## is derived by taking the sum of ##EQU4## and ##EQU5## given by the following equation: ##EQU6## and ##EQU7## with ##EQU8## denoting the error covariance matrix due to temporal noise, and ##EQU9## the error covariance matrix due to spatial noise. H is the stellar measurement matrix, with H.sup.T representing the transpose of this matrix, G is the noise sensitivity matrix and G.sup.T is its transpose, while R is the measurement noise covariance matrix. The R matrix is the primary component in equation (1), the determination of star tracker white and spatial noise attenuation of the Kalman filter. For equation 3 above, .phi. is the state transition matrix while .phi..sup.T is its transpose, .GAMMA. is the process noise sensitivity matrix with .GAMMA..sup.T as the transpose, and Q.sub.n is the error covariance matrix of gyroscope noise as calculated from gyroscope manufacturer specifications. P.sup.+ (t-.DELTA.t) is the error covariance matrix after a given time t-.DELTA.t.
These equations are conventional for the determination of K.sub.c, and typically carried out on a computer aboard the spacecraft. Further details on determining spacecraft attitude can be found in Spacecraft Attitude Determination and Control, Computer Sciences Corporation, Edited by James R. Wertz, 1986, pages 459-469 and 703-709.